Final
Arielle
05/01/2020
Part 1: Neighborhood environments in New York City
Question 1: Run an appropriate unsupervised learning analysis that will address the above research question. Your analysis should include a data-driven approach to determine the optimal number of outputs that are retained/produced by the chosen learning technique.
First, I read in the nyc environment dataset and removed any of the NAs in the dataset (there were no missing data in this data set). I then checked if scaling was needed by looking at the means and standard devations. Since the means and SDs were similar to each other I did not think that it was necessary to scale the data.
nyc.env<-read.csv("nyc_env_correct.csv", header=TRUE)
nyc.env.nomiss<-na.omit(nyc.env)
#Check means and SDs to determine if scaling is necessary
colMeans(nyc.env.nomiss, na.rm=TRUE)## Pct.Low.Inc Diesel.Conc
## 0.3663891 3.9260364
## NPL.Site.Count..wt.by.dist Pct.pre1960.Housing
## 0.1573208 0.6720128apply(nyc.env.nomiss, 2, sd, na.rm=TRUE)## Pct.Low.Inc Diesel.Conc
## 0.1932175 1.5077004
## NPL.Site.Count..wt.by.dist Pct.pre1960.Housing
## 0.1724710 0.2312597A clustering analysis was done next using k-means clustering to assess if there are any clusters in the data and where they are. The gap statistic determined that 8 clusters were needed for this data and that was entered to the final cluster model.
set.seed(100)
clusters<-kmeans(nyc.env, 4, nstart=25)
str(clusters)## List of 9
## $ cluster : int [1:2140] 1 2 2 2 1 3 1 2 1 4 ...
## $ centers : num [1:4, 1:4] 0.383 0.302 0.355 0.406 2.22 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:4] "1" "2" "3" "4"
## .. ..$ : chr [1:4] "Pct.Low.Inc" "Diesel.Conc" "NPL.Site.Count..wt.by.dist" "Pct.pre1960.Housing"
## $ totss : num 5120
## $ withinss : num [1:4] 59.1 54.6 73.2 115.7
## $ tot.withinss: num 303
## $ betweenss : num 4818
## $ size : int [1:4] 307 343 815 675
## $ iter : int 2
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"clusters## K-means clustering with 4 clusters of sizes 307, 343, 815, 675
##
## Cluster means:
## Pct.Low.Inc Diesel.Conc NPL.Site.Count..wt.by.dist Pct.pre1960.Housing
## 1 0.3826832 2.219956 0.1859193 0.4013800
## 2 0.3017552 1.324008 0.1125524 0.3606563
## 3 0.3547306 4.568935 0.1321465 0.8047739
## 4 0.4058986 5.247962 0.1974583 0.7930192
##
## Clustering vector:
## [1] 1 2 2 2 1 3 1 2 1 4 1 1 4 1 4 1 1 1 3 1 1 1 3 1 3 3 4 4 4 1 4 3 4 3
## [35] 1 3 4 1 4 4 1 1 3 1 3 4 2 1 3 1 3 1 4 2 4 3 1 4 3 3 1 3 3 2 1 1 2 1
## [69] 1 1 1 1 1 1 2 1 2 4 4 2 1 4 2 4 4 4 4 4 3 1 4 1 2 1 2 4 3 3 1 3 1 1
## [103] 1 4 4 4 1 4 4 4 4 4 3 1 4 4 3 4 4 4 3 4 1 3 1 1 1 4 3 3 1 3 4 1 4 4
## [137] 3 3 4 3 4 3 4 4 3 4 3 3 3 4 4 4 4 3 4 4 3 4 3 4 4 4 4 3 4 4 4 3 4 3
## [171] 4 4 3 4 4 3 4 3 3 4 3 4 3 4 3 4 4 4 3 4 2 3 3 3 4 3 3 2 2 3 3 3 3 3
## [205] 3 3 3 3 3 2 2 2 2 3 3 2 2 2 2 2 3 3 3 3 2 3 3 3 3 3 2 2 3 3 3 3 3 3
## [239] 2 3 2 2 3 3 3 3 2 1 3 1 1 3 1 4 1 2 1 4 3 1 3 4 3 1 3 2 4 2 4 3 4 4
## [273] 4 2 3 3 3 2 3 3 3 3 1 2 3 3 3 4 4 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3
## [307] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 4 4 4 4
## [341] 4 4 1 1 1 1 2 4 1 3 4 4 3 1 4 3 4 3 1 2 4 4 1 2 4 2 4 4 3 1 2 2 3 3
## [375] 2 2 3 4 3 3 4 3 4 3 4 3 4 2 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [409] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [443] 4 4 4 4 4 4 4 4 4 4 4 4 4 1 4 4 4 1 4 4 4 4 1 4 1 4 1 4 4 4 4 4 4 4
## [477] 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 1
## [511] 4 4 4 4 4 4 4 4 4 4 1 4 4 4 4 1 4 4 3 4 3 4 3 4 3 4 3 4 4 4 1 4 1 1
## [545] 4 1 4 3 4 3 4 3 4 3 4 1 4 3 4 3 4 3 4 3 1 1 1 1 4 3 3 4 3 4 3 4 3 1
## [579] 1 1 3 4 3 4 1 4 3 4 2 1 4 1 3 1 1 3 3 2 3 3 3 3 3 3 3 2 3 2 3 2 3 3
## [613] 3 3 3 3 2 3 2 3 3 1 2 3 2 3 2 3 2 3 2 2 2 1 3 3 2 3 2 3 2 2 4 3 3 4
## [647] 3 3 4 4 3 3 2 3 4 3 3 4 3 4 3 4 1 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 2 4
## [681] 3 4 2 4 3 4 4 3 4 2 4 2 4 3 4 3 4 1 4 3 4 3 4 3 4 2 4 3 4 3 4 3 4 3
## [715] 4 3 4 3 4 3 1 1 4 3 3 4 3 3 3 1 4 4 1 4 1 4 4 1 4 3 4 3 3 3 4 3 1 3
## [749] 1 3 1 3 4 4 4 4 4 3 4 4 4 3 1 3 1 3 3 3 1 3 3 1 3 4 3 1 3 3 4 3 4 3
## [783] 4 4 3 4 3 4 3 1 3 4 3 4 1 3 1 4 1 4 1 4 1 4 4 4 4 4 4 4 1 4 4 4 4 4
## [817] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 4 1 4 4 4 4 4 4 4 4 1 4 4 1 2
## [851] 3 3 3 2 3 1 4 3 4 4 4 4 4 3 3 3 3 3 3 3 4 3 2 3 3 3 3 3 3 3 3 3 3 2
## [885] 2 2 3 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [919] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [953] 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 3 2
## [987] 2 2 3 2 3 3 3 3 3 3 3 3 3 2 2 2 2 3 3 2 3 2 2 3 2 2 2 3 2 2 2 2 2 2
## [1021] 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 2 2 2 3 3 3 3 2 2 2 3 3 3 3
## [1055] 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 2 1
## [1089] 4 3 2 1 4 1 1 4 1 1 1 4 4 1 1 1 1 4 4 4 1 1 1 1 4 1 1 1 1 4 4 1 1 4
## [1123] 4 4 1 4 1 4 1 4 4 1 4 4 4 4 1 4 4 4 1 1 4 1 1 1 4 4 4 1 4 1 4 1 4 4
## [1157] 1 1 4 1 4 4 1 4 4 1 3 4 4 4 1 1 1 1 4 1 4 1 4 4 4 1 4 1 1 1 3 4 1 1
## [1191] 1 4 1 1 1 4 1 1 1 1 1 1 4 1 1 1 1 1 4 1 4 4 1 1 1 4 4 1 4 1 1 1 1 1
## [1225] 1 4 4 4 4 4 1 4 1 1 1 1 1 1 4 1 4 4 1 1 1 1 1 1 1 4 4 1 4 4 4 4 1 3
## [1259] 1 4 4 3 4 3 1 3 1 3 1 1 3 2 4 3 4 2 4 3 1 2 4 3 1 3 1 3 4 4 1 3 1 1
## [1293] 1 1 3 4 4 4 1 3 4 4 4 4 1 3 1 4 1 1 4 1 4 1 4 4 1 4 1 4 4 4 4 4 4 4
## [1327] 4 1 4 4 4 4 1 4 1 1 4 1 4 1 4 1 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 1 4 4
## [1361] 4 4 4 4 4 4 4 2 4 4 3 3 1 1 1 1 1 3 3 3 4 3 3 3 3 3 3 1 3 3 3 4 3 3
## [1395] 3 4 3 1 3 3 2 4 3 3 3 4 2 4 4 2 4 3 4 3 4 4 2 4 4 2 2 4 4 4 1 4 4 4
## [1429] 1 4 1 1 4 3 4 3 1 3 4 3 4 3 1 3 4 3 4 3 4 3 3 3 4 2 4 3 4 3 4 3 4 3
## [1463] 4 3 4 3 4 3 3 3 3 3 3 1 3 1 3 3 4 3 3 4 3 4 4 3 4 3 4 3 4 3 4 3 4 3
## [1497] 3 4 4 4 3 3 3 4 3 1 3 3 3 3 4 3 4 4 3 4 2 3 4 4 3 4 3 4 3 3 3 3 3 1
## [1531] 3 3 4 3 3 3 3 3 1 3 3 1 3 3 4 3 3 3 4 1 4 4 4 4 4 2 4 4 3 4 3 4 2 4
## [1565] 2 4 2 4 4 4 2 4 3 4 2 4 3 4 2 4 3 4 3 4 2 4 4 3 4 4 4 2 4 4 2 4 4 1
## [1599] 4 2 4 2 4 3 2 2 4 4 4 4 3 4 4 3 4 4 4 3 4 3 4 1 4 3 4 4 4 1 3 3 3 4
## [1633] 3 1 3 1 3 4 4 4 4 4 3 1 3 2 4 3 3 1 1 1 3 1 1 3 2 3 3 3 3 3 1 3 1 3
## [1667] 1 3 1 2 4 3 4 2 4 3 4 3 4 3 1 1 3 3 4 3 4 3 1 3 4 4 3 1 4 4 3 1 4 3
## [1701] 3 3 3 1 3 4 3 3 4 3 1 4 3 4 3 3 4 3 3 4 3 3 3 4 3 3 4 3 3 3 3 3 3 3
## [1735] 3 3 3 3 3 3 3 3 3 3 2 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [1769] 3 3 4 3 4 1 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3
## [1803] 3 3 3 3 3 3 3 2 1 4 4 3 1 4 2 1 4 4 4 4 4 3 3 1 4 2 4 2 4 4 4 4 4 4
## [1837] 4 4 4 4 4 4 1 4 4 3 4 3 3 3 4 4 4 4 3 3 3 3 3 3 3 3 3 3 2 3 3 2 3 2
## [1871] 2 2 2 2 2 2 3 3 3 3 3 3 3 2 3 3 1 2 2 2 3 3 2 3 2 1 3 3 2 2 1 2 2 1
## [1905] 3 3 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 3 2 2 2 2 2 2 2 2 2 3
## [1939] 2 2 3 3 3 2 3 3 3 2 3 3 2 3 3 3 3 3 3 3 3 3 3 2 2 2 3 3 2 2 2 3 2 3
## [1973] 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 3 3 3 3 3
## [2007] 3 3 3 3 3 3 3 3 3 2 2 3 3 2 2 3 2 3 2 3 3 3 3 3 3 3 2 2 2 2 2 3 2 2
## [2041] 2 2 2 2 2 2 2 3 2 2 2 3 2 3 2 2 3 2 2 2 2 2 3 2 2 2 2 3 3 3 2 2 2 2
## [2075] 2 2 2 3 3 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
## [2109] 2 3 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 1
##
## Within cluster sum of squares by cluster:
## [1] 59.07688 54.63678 73.23830 115.71393
## (between_SS / total_SS = 94.1 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"fviz_cluster(clusters, data=nyc.env)
#Conduct a gap_statistic analysis to determine optimal number of clusters
gap_stat<-clusGap(nyc.env, FUN=kmeans, nstart=25, K.max=9, B=50)
print(gap_stat, method="firstmax")## Clustering Gap statistic ["clusGap"] from call:
## clusGap(x = nyc.env, FUNcluster = kmeans, K.max = 9, B = 50, nstart = 25)
## B=50 simulated reference sets, k = 1..9; spaceH0="scaledPCA"
## --> Number of clusters (method 'firstmax'): 8
## logW E.logW gap SE.sim
## [1,] 6.818152 7.377546 0.5593943 0.005985380
## [2,] 5.854314 7.149895 1.2955808 0.005929672
## [3,] 5.647194 6.991090 1.3438961 0.005486990
## [4,] 5.502733 6.854749 1.3520154 0.004973083
## [5,] 5.413318 6.794889 1.3815714 0.004773167
## [6,] 5.356176 6.742573 1.3863974 0.004890486
## [7,] 5.304725 6.698461 1.3937361 0.004408503
## [8,] 5.262788 6.658238 1.3954499 0.003981742
## [9,] 5.248153 6.621767 1.3736139 0.004295583clusters.1<-kmeans(nyc.env, 8, nstart=25)
str(clusters.1)## List of 9
## $ cluster : int [1:2140] 4 4 4 4 5 1 5 4 5 8 ...
## $ centers : num [1:8, 1:4] 0.487 0.245 0.276 0.42 0.319 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:8] "1" "2" "3" "4" ...
## .. ..$ : chr [1:4] "Pct.Low.Inc" "Diesel.Conc" "NPL.Site.Count..wt.by.dist" "Pct.pre1960.Housing"
## $ totss : num 5120
## $ withinss : num [1:8] 27.6 24.6 23.5 33.2 38.2 ...
## $ tot.withinss: num 188
## $ betweenss : num 4933
## $ size : int [1:8] 473 276 420 280 234 2 136 319
## $ iter : int 3
## $ ifault : int 0
## - attr(*, "class")= chr "kmeans"clusters.1## K-means clustering with 8 clusters of sizes 473, 276, 420, 280, 234, 2, 136, 319
##
## Cluster means:
## Pct.Low.Inc Diesel.Conc NPL.Site.Count..wt.by.dist Pct.pre1960.Housing
## 1 0.4872041 4.782577 0.1515335 0.8077177
## 2 0.2448580 5.110912 0.2557669 0.8033957
## 3 0.2759884 4.408634 0.1095319 0.7970079
## 4 0.4198341 1.620486 0.1240337 0.4135573
## 5 0.3190396 2.326111 0.1906905 0.3905817
## 6 0.1281830 5.238331 3.8956107 0.8469171
## 7 0.2115952 1.011876 0.1200858 0.2921808
## 8 0.4667308 5.426907 0.1408217 0.7866891
##
## Clustering vector:
## [1] 4 4 4 4 5 1 5 4 5 8 5 4 1 5 1 5 4 5 1 5 4 5 1 4 1 1 1 8 1 5 1 1 8 1
## [35] 5 1 8 4 8 8 4 5 1 5 1 1 4 5 1 4 1 4 1 4 1 1 4 1 1 1 4 1 1 4 4 4 7 4
## [69] 4 4 4 4 4 4 4 4 4 1 1 7 5 8 4 8 8 8 1 1 1 4 1 4 4 4 7 1 1 1 5 1 5 5
## [103] 5 8 8 8 5 8 8 8 8 8 1 5 8 8 1 8 8 8 1 8 4 1 5 5 4 8 1 1 5 1 8 5 8 8
## [137] 1 1 8 1 8 1 8 8 1 8 1 1 1 8 8 8 8 1 8 8 1 8 1 8 8 8 8 1 1 8 8 1 8 1
## [171] 8 8 1 8 8 1 8 1 1 8 1 8 1 8 1 8 2 8 1 1 4 1 1 1 1 1 1 4 4 1 3 3 1 1
## [205] 3 1 3 1 3 4 4 4 4 3 1 4 4 4 4 4 3 3 3 3 7 3 1 3 1 1 4 4 1 3 1 3 1 3
## [239] 4 3 4 7 3 3 3 3 4 4 3 4 4 3 4 1 4 4 4 1 3 4 3 1 1 4 3 4 8 4 8 3 8 1
## [273] 1 4 1 3 1 4 1 3 1 3 5 4 1 3 1 1 1 1 1 1 3 1 1 3 1 1 3 4 3 1 3 1 3 3
## [307] 3 3 3 3 3 1 3 3 1 1 3 1 3 1 3 3 3 3 3 3 3 3 3 1 3 4 4 4 7 7 8 1 2 2
## [341] 2 2 5 5 5 5 4 1 5 1 8 8 3 5 2 3 2 3 5 4 2 2 5 4 2 4 2 2 3 5 4 4 3 3
## [375] 4 4 1 2 1 1 2 1 2 3 2 1 2 4 2 1 1 6 1 6 1 1 1 1 2 1 1 1 1 1 1 1 2 1
## [409] 1 1 1 1 1 1 1 2 1 2 1 2 1 1 5 2 2 2 1 2 2 2 2 2 8 2 8 2 8 2 8 2 2 2
## [443] 8 2 8 2 8 2 2 2 2 2 2 2 2 5 2 8 2 5 2 8 2 8 5 2 5 8 5 8 2 8 2 8 8 8
## [477] 2 8 8 2 1 5 1 2 8 2 8 2 8 2 8 5 8 2 8 2 2 2 8 1 1 1 2 1 1 1 1 1 1 4
## [511] 1 1 1 1 2 1 2 1 2 1 5 1 1 1 2 5 1 1 1 8 1 8 1 8 1 8 1 8 1 8 4 8 4 4
## [545] 8 4 8 1 8 1 8 1 8 1 8 4 8 1 8 1 8 1 8 1 5 4 5 4 8 1 1 2 1 8 1 8 1 5
## [579] 4 5 1 8 1 8 4 8 1 2 4 5 1 5 1 5 4 1 1 4 1 1 1 1 1 1 1 4 1 4 1 4 1 1
## [613] 1 3 1 1 4 1 4 1 1 4 4 1 4 1 4 1 4 1 4 4 4 4 3 1 4 1 4 1 4 4 1 3 1 2
## [647] 1 1 2 1 1 1 4 1 8 1 1 2 1 2 1 2 4 8 1 8 1 8 1 2 1 8 1 8 1 8 1 8 4 8
## [681] 1 2 4 8 1 2 8 1 8 4 8 4 8 1 8 1 8 4 8 1 8 1 8 1 8 4 8 1 8 1 8 1 8 1
## [715] 8 1 8 1 8 1 5 5 1 2 1 2 1 1 1 4 1 1 5 1 4 1 1 5 1 1 2 1 1 1 1 1 4 1
## [749] 4 1 4 1 2 1 2 1 2 2 2 2 2 2 4 1 4 1 1 1 4 1 1 5 1 2 1 5 1 1 2 1 2 1
## [783] 8 8 1 8 1 8 1 5 1 8 1 8 5 1 5 8 5 8 5 8 5 8 8 8 8 8 2 8 5 8 8 8 8 8
## [817] 8 8 2 8 2 2 2 2 2 1 8 2 8 2 2 8 8 8 5 2 5 8 2 2 2 2 2 2 2 4 2 1 4 4
## [851] 1 1 1 4 1 4 1 1 2 2 2 2 2 1 1 1 3 3 3 3 2 1 4 3 3 3 3 3 3 3 3 3 3 4
## [885] 4 4 3 4 4 4 7 4 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
## [919] 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 3 3 1 3 3
## [953] 3 1 1 4 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 1 4
## [987] 4 4 3 4 3 3 3 3 3 1 3 1 3 4 4 4 4 3 3 4 3 4 4 1 4 4 4 3 4 4 4 4 4 4
## [1021] 4 4 3 4 4 4 4 4 4 4 7 7 4 4 7 4 3 3 1 1 4 4 4 3 3 1 3 4 4 4 3 1 1 1
## [1055] 4 4 4 4 4 4 4 4 1 1 1 1 3 1 1 3 4 3 1 1 3 3 1 1 3 1 1 3 3 4 1 3 7 5
## [1089] 2 1 4 5 8 5 5 8 5 5 5 8 2 5 5 5 5 8 8 8 5 5 5 5 8 5 5 5 5 8 8 5 5 8
## [1123] 2 8 5 8 5 8 5 8 8 5 8 8 2 2 5 2 8 8 5 5 2 5 5 5 2 8 8 5 8 5 2 5 2 8
## [1157] 5 5 8 5 2 8 5 8 8 5 3 8 8 8 5 5 5 5 8 5 8 5 8 8 8 5 8 5 5 5 3 8 5 5
## [1191] 5 8 5 5 5 8 5 5 5 5 5 5 2 5 5 5 5 5 8 5 8 2 5 5 5 8 2 5 2 5 5 5 5 5
## [1225] 5 8 2 8 2 2 4 2 5 5 5 5 5 5 2 5 2 2 5 5 5 5 5 5 4 2 2 5 2 2 2 2 5 2
## [1259] 4 2 1 2 1 2 4 2 4 2 4 5 2 4 2 2 1 4 8 2 5 4 1 1 5 1 5 2 8 1 5 1 5 5
## [1293] 5 5 1 2 2 2 5 3 8 2 8 8 5 1 5 8 5 5 2 5 2 4 8 8 5 2 4 8 2 8 8 8 2 8
## [1327] 8 5 2 8 8 8 5 2 5 5 8 5 2 5 8 5 8 8 8 8 8 2 2 5 8 8 8 8 8 8 8 5 8 8
## [1361] 8 8 8 8 8 8 8 4 8 2 1 1 5 5 5 5 5 3 3 3 8 3 3 3 3 1 3 5 3 3 3 8 3 3
## [1395] 3 8 3 5 3 3 4 8 3 3 3 8 4 2 8 7 8 3 2 3 8 8 4 2 2 7 7 2 2 2 5 2 2 2
## [1429] 5 2 5 5 8 3 1 3 5 3 2 3 2 3 5 3 2 3 2 3 2 3 3 3 2 4 2 3 1 3 2 3 2 3
## [1463] 2 3 2 3 2 3 3 3 3 3 3 5 1 5 1 3 2 3 3 2 3 2 2 3 2 3 2 3 2 3 2 3 8 3
## [1497] 3 8 8 8 3 3 3 8 3 5 3 3 3 3 8 3 8 8 3 8 4 3 8 8 3 8 3 8 3 3 3 3 3 5
## [1531] 3 3 2 3 3 1 3 1 5 1 3 5 1 3 8 3 1 1 8 5 8 8 8 8 8 4 8 8 3 8 3 8 4 8
## [1565] 4 8 4 8 8 8 4 8 3 8 4 2 3 2 4 2 3 2 3 2 4 2 2 3 2 8 8 4 2 2 7 2 2 5
## [1599] 2 7 2 7 2 3 7 7 2 2 2 2 3 2 2 3 8 2 2 3 2 3 2 5 8 3 8 8 8 5 3 3 3 8
## [1633] 3 5 3 5 3 8 8 8 8 8 3 5 3 4 8 3 3 5 5 5 3 5 5 3 4 3 1 3 3 3 5 3 5 3
## [1667] 5 3 5 4 8 3 8 4 8 3 8 3 8 3 5 5 3 3 2 3 8 3 5 3 8 8 3 5 8 2 3 5 8 3
## [1701] 3 3 3 5 3 2 3 3 2 3 5 8 3 8 3 3 2 3 3 2 3 3 3 2 3 3 1 3 3 1 3 3 1 1
## [1735] 3 1 1 3 1 3 1 3 1 3 4 3 4 3 3 1 3 1 3 1 1 3 1 3 1 1 1 1 3 1 3 1 3 2
## [1769] 3 3 2 3 2 4 3 5 3 3 3 1 3 3 3 3 3 1 3 1 3 1 7 3 3 3 3 3 3 3 3 1 2 3
## [1803] 3 3 3 2 3 3 3 7 5 2 2 3 5 2 7 5 2 2 2 2 2 3 3 5 2 7 2 7 2 2 2 2 2 2
## [1837] 2 2 2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 1 1 1 1 1 1 4 1 1 4 3 4
## [1871] 4 4 4 4 4 4 1 1 3 3 1 3 3 4 3 3 4 4 4 4 1 3 4 3 4 4 1 3 4 7 4 7 7 5
## [1905] 3 1 3 4 7 7 7 4 7 7 7 4 1 7 7 7 7 7 4 4 7 3 7 3 7 7 7 7 7 7 7 7 7 3
## [1939] 7 7 3 3 3 4 3 3 3 7 3 3 7 3 3 3 3 3 3 3 3 3 3 4 4 4 3 3 4 4 4 3 4 3
## [1973] 3 3 3 3 4 3 3 3 1 1 3 3 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 3 3 3 3 3
## [2007] 3 3 3 3 3 3 3 3 3 4 7 3 3 7 7 3 7 3 7 3 3 3 3 3 3 3 4 7 4 7 4 3 4 7
## [2041] 7 7 4 4 7 7 7 3 7 7 7 3 7 3 7 7 3 4 4 7 7 4 3 7 7 7 7 3 3 3 7 7 7 7
## [2075] 7 7 4 3 3 7 7 7 7 7 7 7 3 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
## [2109] 7 3 7 7 7 7 3 4 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4 7 7 7 7 3 4 5
##
## Within cluster sum of squares by cluster:
## [1] 27.645832 24.618364 23.497208 33.164919 38.231521 4.285446 11.894939
## [8] 24.261436
## (between_SS / total_SS = 96.3 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"fviz_cluster(clusters.1, data=nyc.env)
The next thing that I did was Hierarichical clustering setting the distance Euclidian methods since the data was all continuous and numeric. A dissimilarity matrix was used to get the distance and looked at the difference clustering methods: Complete, Single, and average A gap statistic was also used to get the optimal number of clusters.
set.seed(100)
# Create Dissimilarity matrix
diss.matrix <- dist(nyc.env, method = "euclidean")
gap_stat <- clusGap(nyc.env, FUN = hcut, nstart = 25, K.max = 10, B = 50, mc_metric = "euclidean")
fviz_gap_stat(gap_stat)
gap_stat1 <- clusGap(nyc.env, FUN = hcut, nstart = 25, K.max = 10, B = 50, mc_metric = "euclidean", method = "single")
fviz_gap_stat(gap_stat1)
# Create Dissimilarity matrix
diss.matrix <- dist(nyc.env, method = "euclidean")
# Hierarchical clustering using Single Linkage
hc1 <- hclust(diss.matrix, method = "single" )
groups.1<-cutree(hc1,4)
aggregate(nyc.env,list(groups.1),mean)## Group.1 Pct.Low.Inc Diesel.Conc NPL.Site.Count..wt.by.dist
## 1 1 0.33997812 1.747171 0.1472041
## 2 2 0.37824636 4.876062 0.1567154
## 3 3 0.09781744 5.234196 2.4328626
## 4 4 0.15854864 5.242467 5.3583589
## Pct.pre1960.Housing
## 1 0.3798904
## 2 0.7993850
## 3 0.8933042
## 4 0.8005300# Plot the obtained dendrogram using Single
plot(hc1, cex = 0.6, hang = -1)
gap_stat2 <- clusGap(nyc.env, FUN = hcut, nstart = 25, K.max = 10, B = 50, mc_metric = "euclidean", method = "complete")
fviz_gap_stat(gap_stat2)
# Hierarchical clustering using Complete Linkage
hc2 <- hclust(diss.matrix, method = "complete" )
groups.2 <-cutree(hc2,4)
aggregate(nyc.env,list(groups.2),mean)## Group.1 Pct.Low.Inc Diesel.Conc NPL.Site.Count..wt.by.dist
## 1 1 0.3422037 1.728378 0.1474176
## 2 2 0.3782615 4.876946 0.1582655
## 3 3 0.1585486 5.242467 5.3583589
## 4 4 0.1708487 3.169033 0.1314285
## Pct.pre1960.Housing
## 1 0.3801287
## 2 0.7999302
## 3 0.8005300
## 4 0.3348217# Plot the obtained dendrogram using Complete
plot(hc2, cex = 0.6, hang = -1)
gap_stat3 <- clusGap(nyc.env, FUN = hcut, nstart = 25, K.max = 10, B = 50, mc_metric = "euclidean", method = "average")
fviz_gap_stat(gap_stat3)
# Hierarchical clustering using Average Linkage
hc3 <- hclust(diss.matrix, method = "average" )
groups.3<-cutree(hc3,4)
aggregate(nyc.env,list(groups.3),mean)## Group.1 Pct.Low.Inc Diesel.Conc NPL.Site.Count..wt.by.dist
## 1 1 0.3399781 1.747171 0.1472041
## 2 2 0.3784319 4.875831 0.1550308
## 3 3 0.1928457 5.109687 1.7498787
## 4 4 0.1585486 5.242467 5.3583589
## Pct.pre1960.Housing
## 1 0.3798904
## 2 0.7993745
## 3 0.8358926
## 4 0.8005300# Plot the obtained dendrogram using Average
plot(hc3, cex = 0.6, hang = -1)
Question 2: Describe the outputs of the analysis in terms of their composition of the input features.
The optimal number of cluster based on the k means clustering plot are eight cluster, this is inconsistent with the optimal number of cluster based on hierarchical clustering. For this type of clustering, the gap statistic stated that five was the optimal number of cluster to have. Five clusters was consistent acroos the different types of linkage methods, single, complete and average. Although the cluster dendrograms all look different the results from all of them are the same.
The means for perecnt of low income and percentage of housing stock built before 1960 are similar across all the linkaage methods. The means observed were similar to each other, there was a little more varaition in the means but not a huge varaition for air concentration of diesal extract and proximity to hazardous waste sites.
Question 3: List a subsequent research question that could be addressed using the output of this analysis. The output can be used as an exposure, outcome or confounding variable. State what type of research question it is: descriptive, explanatory or predictive.
A subsequential research question that can be addressed using the outbut of this analysis is a explanatory question which is if a proportion of housing stocking built before 1960 as a proxy for potential lead exposure is associated with increase ambient air concentrations of diesel exhaust, while controling for proportion of neighborhood with household income lwoer than the city median.
Part 2: Choose your own supervised adventure
B) Researchers are interested in uncovering nutritional factors that influence the development of diabetes. To generate hypotheses to guide future research, they ask you to utilize feature selection methods to identify the factors that are most relevant to fasting blood glucose. (The dataset you are given is glucose.csv.) You should try two different algorithms for feature selection and comment if they identify the same set of variables as being important for serum glucose.
The first thing that will be done is import and clean the data.
glucose.raw<-read.csv("glucose.csv", header=TRUE)
glucose =
glucose.raw %>%
drop_na() %>%
janitor::clean_names()Next I will partition the data so that there is a 70/30 split and set the seed to 100.
set.seed(100)
training.data.glucose<-glucose$lbxsgl %>% createDataPartition(p=0.7, list=F)
train.data.glucose<-glucose[training.data.glucose, ]
test.data.glucose<-glucose[-training.data.glucose, ]
#Store outcome
glucose.train<-train.data.glucose$lbxsgl
glucose.test<-test.data.glucose$lbxsgl
# Store the outcome in one train and test and the predictors in another
#model matrix- will create indicator variables for categorical varaibles, it does not do anything to the continuous variables
x.train<-model.matrix(lbxsgl~., train.data.glucose)[,-1]
x.test<-model.matrix(lbxsgl~., test.data.glucose)[,-1]The next thing that I did was create different regression trees to find the one with the best fit. I tried different CPs to find the best one. I double checked this using caret to see if I got similar results.
#Regression Tree 1-default values of rpart
tree.glucose<-rpart(lbxsgl ~ ., data=train.data.glucose, method="anova")
plot(tree.glucose, uniform=TRUE)
text(tree.glucose, use.n=TRUE, all=TRUE, cex=0.8)
printcp(tree.glucose)##
## Regression tree:
## rpart(formula = lbxsgl ~ ., data = train.data.glucose, method = "anova")
##
## Variables actually used in tree construction:
## [1] bmxwaist lbxsse ridageyr x
##
## Root node error: 921862/2416 = 381.57
##
## n= 2416
##
## CP nsplit rel error xerror xstd
## 1 0.054087 0 1.00000 1.00075 0.13340
## 2 0.021376 1 0.94591 0.95737 0.13163
## 3 0.013929 4 0.88179 0.95906 0.13120
## 4 0.010000 5 0.86786 0.94416 0.12774plotcp(tree.glucose)
print(tree.glucose)## n= 2416
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 2416 921862.30 93.78891
## 2) ridageyr< 41.5 1387 340232.70 89.87599
## 4) bmxwaist< 100.75 1053 133523.20 87.83761 *
## 5) bmxwaist>=100.75 334 188540.50 96.30240
## 10) lbxsse< 147.45 298 69364.45 94.48658 *
## 11) lbxsse>=147.45 36 110060.00 111.33330
## 22) x>=1368.5 29 26209.79 96.72414 *
## 23) x< 1368.5 7 52018.86 171.85710 *
## 3) ridageyr>=41.5 1029 531768.90 99.06317
## 6) bmxwaist< 92.85 366 80156.11 94.30874 *
## 7) bmxwaist>=92.85 663 438772.40 101.68780 *rpart.plot(tree.glucose)
#Regression Tree 2- varying values in rpart.control, specifically going to cp=0.001, to find minimum cv-error
tree.glucose.1<-rpart(lbxsgl ~ ., data=train.data.glucose, method="anova", control=rpart.control(cp=0.001))
plotcp(tree.glucose.1)
rpart.plot(tree.glucose.1)
printcp(tree.glucose.1)##
## Regression tree:
## rpart(formula = lbxsgl ~ ., data = train.data.glucose, method = "anova",
## control = rpart.control(cp = 0.001))
##
## Variables actually used in tree construction:
## [1] bmxbmi bmxht bmxwaist bmxwt lbxlyc lbxmg lbxscu
## [8] lbxsse lbxszn riagendr ridageyr ridreth1 x
##
## Root node error: 921862/2416 = 381.57
##
## n= 2416
##
## CP nsplit rel error xerror xstd
## 1 0.0540870 0 1.00000 1.00073 0.13329
## 2 0.0213757 1 0.94591 0.95896 0.13027
## 3 0.0139288 4 0.88179 0.97858 0.12850
## 4 0.0072132 5 0.86786 1.01453 0.12867
## 5 0.0071002 10 0.83179 1.05593 0.12974
## 6 0.0056439 17 0.78209 1.05906 0.12998
## 7 0.0036642 18 0.77645 1.05516 0.12792
## 8 0.0035573 19 0.77278 1.07097 0.12854
## 9 0.0032644 20 0.76922 1.07372 0.12855
## 10 0.0029512 21 0.76596 1.07968 0.12884
## 11 0.0028427 22 0.76301 1.08177 0.12897
## 12 0.0028339 26 0.75132 1.08180 0.12897
## 13 0.0027661 27 0.74849 1.08156 0.12903
## 14 0.0025352 30 0.74019 1.09059 0.12938
## 15 0.0023634 31 0.73766 1.10767 0.13036
## 16 0.0023415 32 0.73529 1.10649 0.13035
## 17 0.0023339 33 0.73295 1.10649 0.13035
## 18 0.0022611 34 0.73062 1.10703 0.13035
## 19 0.0020648 35 0.72836 1.10970 0.13040
## 20 0.0019484 38 0.72216 1.11060 0.12979
## 21 0.0019062 39 0.72021 1.10780 0.12800
## 22 0.0018994 40 0.71831 1.10754 0.12800
## 23 0.0017666 41 0.71641 1.11037 0.12825
## 24 0.0017172 45 0.70906 1.11497 0.12840
## 25 0.0016434 48 0.70391 1.11504 0.12840
## 26 0.0015625 49 0.70227 1.11615 0.12851
## 27 0.0015559 50 0.70070 1.11638 0.12833
## 28 0.0015129 54 0.69448 1.11745 0.12842
## 29 0.0014334 55 0.69297 1.11802 0.12840
## 30 0.0013583 56 0.69153 1.12057 0.12839
## 31 0.0013425 59 0.68746 1.12503 0.12813
## 32 0.0012050 60 0.68612 1.12660 0.12775
## 33 0.0011754 61 0.68491 1.13106 0.12788
## 34 0.0011659 62 0.68374 1.13120 0.12788
## 35 0.0011652 63 0.68257 1.13120 0.12788
## 36 0.0011439 65 0.68024 1.13194 0.12787
## 37 0.0011432 66 0.67910 1.13350 0.12788
## 38 0.0011007 68 0.67681 1.13255 0.12766
## 39 0.0010868 69 0.67571 1.13272 0.12766
## 40 0.0010857 72 0.67245 1.13256 0.12766
## 41 0.0010821 73 0.67136 1.13284 0.12770
## 42 0.0010711 74 0.67028 1.13460 0.12770
## 43 0.0010703 78 0.66600 1.13684 0.12770
## 44 0.0010489 80 0.66386 1.14031 0.12772
## 45 0.0010257 81 0.66281 1.14350 0.12773
## 46 0.0010253 82 0.66178 1.14436 0.12779
## 47 0.0010000 83 0.66076 1.14497 0.12778selected.cp<-tree.glucose.1$cptable[which.min(tree.glucose.1$cptable[,"xerror"]), "CP"]
tree.glucose.pruned<-prune(tree.glucose.1, cp=selected.cp)
rpart.plot(tree.glucose.pruned)
#Regression Tree 3-manually setting cp to 1SD greater error than minimum value
tree.glucose.2<-rpart(lbxsgl ~ ., data=train.data.glucose, method="anova", control=rpart.control(cp=0.006665509))
rpart.plot(tree.glucose.2)
print(tree.glucose.2)## n= 2416
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 2416 921862.300 93.78891
## 2) ridageyr< 41.5 1387 340232.700 89.87599
## 4) bmxwaist< 100.75 1053 133523.200 87.83761 *
## 5) bmxwaist>=100.75 334 188540.500 96.30240
## 10) lbxsse< 147.45 298 69364.450 94.48658 *
## 11) lbxsse>=147.45 36 110060.000 111.33330
## 22) x>=1368.5 29 26209.790 96.72414 *
## 23) x< 1368.5 7 52018.860 171.85710 *
## 3) ridageyr>=41.5 1029 531768.900 99.06317
## 6) bmxwaist< 92.85 366 80156.110 94.30874 *
## 7) bmxwaist>=92.85 663 438772.400 101.68780
## 14) x< 4741 656 382603.000 101.37040
## 28) ridreth1>=1.5 579 275652.800 100.22450
## 56) lbxszn>=55.25 570 239681.100 99.82281
## 112) bmxwaist< 126.35 541 208123.400 99.10166
## 224) ridageyr< 69.5 403 95976.460 97.15385 *
## 225) ridageyr>=69.5 138 106152.900 104.78990
## 450) lbxmg>=2.043592 54 9864.833 97.05556 *
## 451) lbxmg< 2.043592 84 90981.240 109.76190
## 902) lbxlyc< 0.3839563 28 3906.107 98.67857 *
## 903) lbxlyc>=0.3839563 56 81915.840 115.30360
## 1806) x< 1740 20 4594.950 101.45000 *
## 1807) x>=1740 36 71350.000 123.00000
## 3614) lbxsse>=128.95 25 12245.840 110.92000 *
## 3615) lbxsse< 128.95 11 47164.730 150.45450 *
## 113) bmxwaist>=126.35 29 26027.790 113.27590 *
## 57) lbxszn< 55.25 9 30054.000 125.66670 *
## 29) ridreth1< 1.5 77 100473.000 109.98700
## 58) riagendr>=1.5 32 9049.500 99.87500 *
## 59) riagendr< 1.5 45 85824.580 117.17780
## 118) lbxscu< 98.4 14 4297.714 98.14286 *
## 119) lbxscu>=98.4 31 74163.420 125.77420
## 238) ridageyr>=53.5 20 8725.200 114.20000 *
## 239) ridageyr< 53.5 11 57887.640 146.81820 *
## 15) x>=4741 7 49911.710 131.42860 *#Fit model to test data and calculate R-squared and MSE
pred.intest<-predict(tree.glucose.2, newdata=test.data.glucose)
r.square.test<-cor(test.data.glucose$lbxsgl, pred.intest)^2
r.square.test## [1] 0.04498644pred.mse<-mean((pred.intest-test.data.glucose$lbxsgl)^2)
#Plot distribution of error (not squared error)
test<-data.frame(pred.intest-test.data.glucose$lbxsgl)
histogram(test$pred.intest...test.data.glucose.lbxsgl)
## Good to see what is happening and making sure you know where you have error, want to see if its normal and if the data is skewwed
tree.glucose.2$variable.importance## ridageyr bmxwaist x seqn bmxbmi lbxsse bmxwt
## 64457.323 47582.261 46811.074 46756.676 34075.066 28304.483 25320.586
## lbxscu lbxlyc lbxszn bmxht ridreth1 riagendr lbxmg
## 18436.316 14785.501 10060.125 9248.844 8020.843 5598.909 5477.824In this section I double checked using caret to see if I got similar results as my regression trees above.
set.seed(100)
train.control<-trainControl(method="cv", number=10)
tree.glucose.3<-train(lbxsgl~ . , data=train.data.glucose, method="rpart",trControl=train.control)
tree.glucose.3$bestTune## cp
## 1 0.01392877rpart.plot(tree.glucose.3$finalModel)
pred.intest.temp<-predict(tree.glucose.3, newdata=test.data.glucose)
r.square.test.temp<-cor(test.data.glucose$lbxsgl, pred.intest.temp)^2
r.square.test.temp## [1] 0.04955636#Specify tuneGrid so caret explores wider variety of cp-values
grid<-expand.grid(cp=seq(0.001,0.1, by=0.001))
tree.glucose.4<-train(lbxsgl ~ ., data=train.data.glucose, method="rpart", trControl=train.control, tuneGrid=grid)
rpart.plot(tree.glucose.4$finalModel)
tree.glucose.4$bestTune## cp
## 23 0.023grid<-expand.grid(.cp=0.0067)
tree.glucose.5<-train(lbxsgl ~ ., data=train.data.glucose, method="rpart", trControl=train.control, tuneGrid=grid)
rpart.plot(tree.glucose.5$finalModel)
pred.intest.2<-predict(tree.glucose.5, newdata=test.data.glucose)
r.square.test.2<-cor(test.data.glucose$lbxsgl, pred.intest.2)^2
r.square.test.2## [1] 0.04498644pred.mse.2<-mean((pred.intest.2-test.data.glucose$lbxsgl)^2)
varImp(tree.glucose.5)## rpart variable importance
##
## Overall
## seqn 100.000
## x 100.000
## lbxscu 55.203
## lbxsse 44.578
## ridageyr 42.895
## bmxht 34.640
## lbxlyc 33.463
## bmxwaist 28.422
## bmxbmi 23.774
## bmxwt 16.232
## lbxszn 4.004
## ridreth1 3.926
## lbxmg 1.580
## riagendr 0.000I then did a linear regression model to see how that model was fitted.
model.glucuse <- lm(lbxsgl ~ ., data=train.data.glucose)
summary(model.glucuse)##
## Call:
## lm(formula = lbxsgl ~ ., data = train.data.glucose)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43.772 -9.014 -2.066 4.697 233.161
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 49.9356330 59.1706995 0.844 0.398795
## x -0.0068140 0.0041561 -1.640 0.101231
## seqn 0.0016057 0.0008884 1.807 0.070841 .
## lbxscu -0.0171197 0.0138677 -1.234 0.217138
## lbxsse 0.0711291 0.0218334 3.258 0.001138 **
## lbxmg -0.2764060 0.2709803 -1.020 0.307820
## lbxlyc 1.3169067 1.2999037 1.013 0.311124
## lbxszn -0.0515764 0.0249400 -2.068 0.038746 *
## bmxwt 0.3232066 0.1577145 2.049 0.040540 *
## bmxht -0.4945555 0.1474998 -3.353 0.000812 ***
## bmxbmi -0.9720705 0.4442199 -2.188 0.028746 *
## bmxwaist 0.2593932 0.0747389 3.471 0.000528 ***
## riagendr -4.2378956 1.0510519 -4.032 5.7e-05 ***
## ridageyr 0.1591642 0.0230109 6.917 5.9e-12 ***
## ridreth1 0.0026783 0.3137063 0.009 0.993189
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.5 on 2401 degrees of freedom
## Multiple R-squared: 0.1087, Adjusted R-squared: 0.1035
## F-statistic: 20.91 on 14 and 2401 DF, p-value: < 2.2e-16rmse(model.glucuse, test.data.glucose)## [1] 16.59664I then fitted a support vector model to compare to the other two models to see which model performed the best.
set.seed (100)
svm.glucose<-svm(lbxsgl ~ ., data=train.data.glucose, kernel="linear", cost=1, scale=TRUE)
print(svm.glucose)##
## Call:
## svm(formula = lbxsgl ~ ., data = train.data.glucose, kernel = "linear",
## cost = 1, scale = TRUE)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: linear
## cost: 1
## gamma: 0.07142857
## epsilon: 0.1
##
##
## Number of Support Vectors: 2005svm.pred<-predict(svm.glucose, newdata=train.data.glucose)
table(svm.pred, train.data.glucose$lbxsgl)##
## svm.pred 51 55 56 57 58 60 61 63 64 65 66 67 68 69 70 71 72 73
## 80.0562078116171 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 80.3913596110989 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 80.5139042665649 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.0510909137322 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
## 81.0707415155938 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.2098924661798 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.3323008567811 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.3406131814013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.4341649480316 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.4380653100961 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.480033115421 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.4874199790237 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.48998537045 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.5208310716737 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.6808033618252 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.6965411229183 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.715866655641 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.7511142855645 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.7631148456107 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.7777055319578 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.9061123313775 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.0292414220675 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.0797427415111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.1268436374399 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 82.1423449459458 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.1954875315059 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.2397793259966 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.244201944717 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.2630172741124 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.2691704231734 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.3230963457374 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.3274174853165 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.3790173536243 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## 82.3902664624284 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.4063762466212 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## 82.4105718963457 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
## 82.4368255439316 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.4854994346157 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.5693477092743 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.5737508295927 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.60250272849 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.6420667381092 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.6697137125483 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## 82.8064482660252 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.866730951776 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.8889726520587 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.9167537431459 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.9516449278206 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.9626246694834 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.9659849882285 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.004021459652 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## 83.0120991196498 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.0292622952407 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.0367251938003 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.0556170398176 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.0614515107972 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.1503272102081 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.1765766883659 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.1902574012681 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.2003256204974 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.2038273956669 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.2464012644528 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.2724851116498 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.2899601715791 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.3025162561076 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.3032408165372 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.3279126207748 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.3313872763176 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.3350099657004 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.3965364820042 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.4135247264096 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.4283297675431 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.4337828112303 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.4490513063826 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.4612113391389 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.4877864977705 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.5008319757203 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.5192375179742 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.535599974862 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.5526344342401 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.5631914377507 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## 83.5750531714831 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.5780737561232 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.5781381202968 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.5839967861379 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 83.6185133029239 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## 89.3140833771628 0 0 0 0 0 0 0 0 0 0 0
## [ reached getOption("max.print") -- omitted 1576 rows ]rmse(svm.glucose, test.data.glucose)## [1] 16.78708features<-x.train
outcome<-train.data.glucose$lbxsgl
svm_tune <- tune(svm, train.x=features, train.y=outcome, kernel="linear", range=list(cost=10^(-1:2)))
summary(svm_tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost
## 100
##
## - best performance: 352.6775
##
## - Detailed performance results:
## cost error dispersion
## 1 0.1 353.0315 141.0055
## 2 1.0 352.8538 140.7250
## 3 10.0 352.7076 140.6454
## 4 100.0 352.6775 140.6988svm.glucose.new<-svm(lbxsgl ~ ., data=train.data.glucose, kernel="linear", cost= 100, scale=TRUE)
print(svm.glucose.new)##
## Call:
## svm(formula = lbxsgl ~ ., data = train.data.glucose, kernel = "linear",
## cost = 100, scale = TRUE)
##
##
## Parameters:
## SVM-Type: eps-regression
## SVM-Kernel: linear
## cost: 100
## gamma: 0.07142857
## epsilon: 0.1
##
##
## Number of Support Vectors: 2006svm.pred.new<-predict(svm.glucose.new, newdata=test.data.glucose)
table(svm.pred.new, test.data.glucose$lbxsgl)##
## svm.pred.new 56 57 58 59 60 62 64 65 66 67 68 69 70 71 72 73 74 75
## 79.4313465942425 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.1896394368928 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 81.9596255715996 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
## 82.0750122790338 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.1332175432839 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.2173933248288 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.2898327641508 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.3093443823574 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.4683868382443 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.5625029331042 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.5815462743339 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## 82.5822503246989 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.6537451889418 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.6598073782148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 82.6676399137133 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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## [ reached getOption("max.print") -- omitted 3 rows ]rmse(svm.glucose.new, test.data.glucose)## [1] 16.79641The support vector machine used the largest cost of 100 that shows there is a lot of misclassiofcation in in this model.